# Category:Inductive Sets

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This category contains results about **Inductive Sets**.

Let $S$ be a set of sets.

Then $S$ is **inductive** if and only if:

\((1)\) | $:$ | $S$ contains the empty set: | \(\ds \quad \O \in S \) | ||||||

\((2)\) | $:$ | $S$ is closed under the successor mapping: | \(\ds \forall x:\) | \(\ds \paren {x \in S \implies x^+ \in S} \) | where $x^+$ is the successor of $x$ | ||||

That is, where $x^+ = x \cup \set x$ |

## Subcategories

This category has the following 2 subcategories, out of 2 total.

## Pages in category "Inductive Sets"

The following 5 pages are in this category, out of 5 total.